The rise of “Multiple devices per user” computing model and the mobility requirement of moving across physical environments bring great challenges to task migration in four aspects: continuity, transparency, heterogeneity and generality. This paper proposes the concept of “virtual user space”, and establishes a task migration framework based on a virtual user space, called TaskShadow-V, to address these challenges. Virtual user space guarantees the continuity of user tasks and capabilities of migrating across mobile devices. Meanwhile, the context-based mechanism of intelligent migration decision-making is proposed to ensure transparency of task migration. This mechanism employs virtual user space as the migrating granularity and uses context information to automatically make the decisions of migration. The study conducts an experiment to verify the effectiveness of proposed TaskShadow-V framework.